Question

If F -1(x) is the inverse of F(x), which statements must be true?

Check all that apply.

A.The range of F -1(x) is the range of F(x).
B.F -1(F(x)) = x
C.The range of F -1(x) is the domain of F(x).
D.F(F -1(x)) = x
E.The domain of F -1(x) is the range of F(x).
F.The domain of F -1(x) is the domain of F(x).

Answer 1

The correct answers are D. B. C. AND E

Answer 2

The inverse function, denoted
`F^(-1)(x),` of a one-to-one function
`F(x)` is defined as

`F^(-1)(x) = \{(y,x) | \text{ such that } y = f(x)\}.`

Main properties:

1.
`F(F^(-1)(x)) = x,` x in the domain of
`F^(-1);`

`F^(-1)(F(x)) = x,` x in the domain of F.

2. The domain of F is equal to the range of
`F^(-1)` and the range of F is equal to the domain of
`F^(-1).`

From these properties you can state that options B, C, D and E are true and points A and F are false.